Profile: 

• Curriculum Vitae (pdf)

• Some of my lectures: Video1, Video2, Video3, Video4, Video5, Video6, Notes1, Notes2, Notes3

• Collaborators: Matt Bainbridge, Gaëtan Borot, Andrei Bud, Qile Chen, Izzet Coskun, Matteo Costantini, Charley Crissman, Gianluca Faraco, Gavril Farkas, Quentin Gendron, Alessandro Giacchetto, Samuel Grushevsky, David Holmes, Jesse Kass, Danilo Lewański, Martin Möller, Ian Morrison, Scott Nollet, Anand Patel, Miguel Prado, Adrien Sauvaget, Johannes Schmitt, Christian Schnell, Nicola Tarasca, Alex Wright, Fei Yu, Don Zagier 

• A poster of descedents of my advisor Joe Harris 

• A blackboard of my research 

Teaching:

• MATH2210: Linear Algebra, Spring 2024, 2020, 2016.

• MATH8865: Topics in Algebraic Geometry, Fall 2023, 2019. Notes 

• MATH8811: Complex Analysis, Spring 2023, 2020, 2018, 2017. Notes

• MATH4410: Differential Equations, Fall 2022. Notes

• MATH8832: Flat Surfaces, Spring 2022.  

• MATH3312: Algebra II, Spring 2022, 2014. Notes

• MATH3311: Algebra I, Fall 2021, 2013. Notes

• MATH3320: Introduction to Analysis, Spring 2021. Notes

• MATH8831: Characteristic Classes, Fall 2020. Notes

• MATH8808: Algebraic Topology, Fall 2018, 2016. Notes

• MATH8890: Graduate Teaching Seminar I, Fall 2018, 2017, 2016.

• MATH1105: Calculus II, Fall 2017, 2012, 2011. Syllabus

• MATH8845: Riemann Surfaces, Fall 2015. Notes

• MATH4460: Complex Variables, Fall 2015. Syllabus

• MATH2216: Introduction to Abstract Mathematics, Fall 2014. Syllabus

• MATH8845: Intersection Theory and Enumerative Geometry, Spring 2014. Notes

• MATH8845: Algebraic Curves, Spring 2013. Notes

• MATH8822: Algebraic Geometry, Spring 2012. Notes

Advising:

• Developing Relationships with Experts, Notices of the AMS, Sep 2019. 

• Miguel Prado, Ph.D., Boston College, 2020-24. 

• Iulia Gheorghita, Ph.D., Boston College, 2017-21.

• Scott Mullane, Ph.D., Boston College, 2012-16.

• Yuecheng Su, Independent Study, Boston College, Spring 2024. 

• Laura Lu, Independent Study, Boston College, Spring 2023. 

• Ricky Li, Independent Study, Boston College, Summer 2022. 

• Ryan Shapiro, Independent Study, Boston College, Fall 2020.

• Tarannum Rahman, Independent Study, Boston College, Spring 2020.

• Wantong Wei, Independent Study, Boston College, Summer 2019.

• Mingzhuo Deng, Independent Study, Boston College, Fall 2018.

• Miqiu Ding, Undergraduate Research Fellowship, Boston College, Summer 2017.

• Haoyuan Jiang, Undergraduate Research Fellowship, Boston College, Summer 2017.

• Daniel Conroy, Independent Study, Boston College, Spring 2017.

• Anthony Hernandez, Independent Study, Boston College, Spring 2016.

• Zhangyang Wei, Undergraduate Research Fellowship, Boston College, Spring 2016.

Papers:

• Counting differentials with fixed residues (with M. Prado) (pdf), preprint. 

• Filtration and splitting of the Hodge bundle on the non-varying strata of quadratic differentials (with F. Yu) (pdf), preprint. 

• Period realization of meromorphic differentials with prescribed invariants (with G. Faraco) (pdf), preprint. 

• A tale of two moduli spaces: logarithmic and multi-scale differentials (with S. Grushevsky, D. Holmes, M. Möller, and J. Schmitt) (pdf), preprint.

• On the Kodaira dimension of moduli spaces of Abelian differentials (with M. Costantini and M. Möller) (pdf), preprint.

• Moduli of differentials and Teichmüller dynamics (with A. Bud) (pdf), preprint.   

• The moduli space of multi-scale differentials (with M. Bainbridge,  Q. Gendron, S. Grushevsky, and M. Möller) (pdf), preprint.

• Surfaces with big anticanonical class (with C. Schnell) (pdf), preprint.

• Nonvarying, affine, and extremal geometry of strata of differentials (pdf), Math. Proc. Camb. Philos. Soc. 176 (2024), no. 2, 361-371.  

• Masur-Veech volumes and intersection theory: the principal strata of quadratic differentials (with M. Möller, A. Sauvaget and an appendix by G. Borot, A. Giacchetto, and D. Lewanski) (pdf), Duke Math. J. 172 (2023), no. 9, 1735-1779.   

• Complete curves in the strata of differentials (pdf), C. R. Math. Acad. Sci. Paris 361 (2023), 371-373. 

• Dynamical invariants and intersection theory on the flex and gothic loci (pdf), Eur. J. Math. 8 (2022), 42-52.  

• Towards a classification of connected components of the strata of k-differentials (with Q. Gendron) (pdf), Doc. Math. 27 (2022), 1031-1100. 

• The WYSIWYG compactification (with A. Wright) (pdf), J. Lond. Math. Soc. 103 (2021), no. 2, 490-515. 

• Masur-Veech volumes and intersection theory on moduli spaces of Abelian differentials (with M. Möller, A. Sauvaget, and D. Zagier) (pdf), Invent. Math. 222 (2020), no. 1, 283-373. 

• Positivity of divisor classes on the strata of differentials (pdf), Q. J. Math. 71 (2020), no. 1, 247-256.  

• Affine geometry of strata of differentials (pdf), J. Inst. Math. Jussieu 18 (2019), no. 6, 1331-1340.

• Principal boundary of moduli spaces of abelian and quadratic differentials (with Q. Chen) (pdf), Ann. Inst. Fourier 69 (2019), no. 1, 81-118.

• Spin and hyperelliptic structures of log twisted differentials (with Q. Chen) (pdf), Selecta Math. (N.S.) 25 (2019), no. 2, 25:20.

• Tautological ring of strata of differentials (pdf), Manuscripta Math. 158 (2019), no. 3-4, 345-351.

• Strata of k-differentials (with M. Bainbridge, Q. Gendron, S. Grushevsky, and M. Möller) (pdf), Algebr. Geom. 6 (2019), no. 2, 196-233.

• Moduli of differentials (pdf), Oberwolfach Rep. 15 (2018), no. 3.

• Compactification of strata of abelian differentials (with M. Bainbridge, Q. Gendron, S. Grushevsky, and M. Möller) (pdf), Duke. Math. J. 167 (2018), no. 12, 2347-2416.

• Quasimodularity and large genus limits of Siegel-Veech constants (with M. Möller and D. Zagier) (pdf), J. Amer. Math. Soc. 31 (2018), no. 4, 1059-1163.

• An extremal effective survey about extremal effective cycles in moduli spaces of curves (pdf), Abel Symp. 14 (2018), 65-74. 

• Degenerations of Abelian differentials (pdf), J. Diff. Geom. 107 (2017), no. 3, 395-453.

• Teichmüller dynamics in the eyes of an algebraic geometer (pdf), Proc. Sympos. Pure Math. 95 (2017), 171-197.

• Extremality of loci of hyperelliptic curves with marked Weierstrass points (with N. Tarasca) (pdf), Algebra Number Theory 10 (2016), no. 9, 1935-1948.

• Loci of curves with subcanonical points in low genus (with N. Tarasca) (pdf), Math. Z. 284 (2016), no. 3-4, 683-714.

• Extremal effective divisors of Brill-Noether and Gieseker-Petri type in M_{1,n} (with A. Patel) (pdf), Adv. Geom. 16 (2016), no. 2, 231-242.

• Moduli of generalized line bundles on a ribbon (with J. Kass) (pdf), J. Pure Appl. Algebra 220 (2016), no. 2, 822-844.

• Extremal higher codimension cycles on moduli spaces of curves (with I. Coskun) (pdf), Proc. London Math. Soc. (3) 111 (2015), no. 1, 181-204.

• Orbit closures in Teichmüller dynamics and extremal cycles in algebraic geometry (pdf), Oberwolfach Rep. 11 (2014), no. 1.

• Quadratic differentials in low genus: exceptional and non-varying strata (with M. Möller) (pdf), Ann. Sci. Éc. Norm. Supér. (4) 47 (2014), no. 2, 309-369.

• Extremal effective divisors on the moduli space of n-pointed genus one curves (with I. Coskun) (pdf), Math. Ann. 359 (2014), no. 3-4, 891-908.

• Effective divisors on moduli spaces of curves and abelian varieties (with G. Farkas and I. Morrison) (pdf), Clay Math. Proc. 18 (2013), 131-169.

• Strata of abelian differentials and the Teichmüller dynamics (pdf), J. Mod. Dyn. 7 (2013), no. 1, 135-152.

• Covers of the projective line and the moduli space of quadratic differentials (pdf), Geom. Dedicata 163 (2013), no. 1, 105-125.

• Nonvarying sums of Lyapunov exponents of Abelian differentials in low genus (with M. Möller) (pdf), Geom. Topol. 16 (2012), no. 4, 2427-2479.

• Detaching embedded points (with S. Nollet) (pdf), Algebra Number Theory 6 (2012), no. 4, 731-756.

• Towards Mori's program for the moduli space of stable maps (with I. Coskun and an appendix by C. Crissman) (pdf), Amer. J. Math. 133 (2011), no. 5, 1389-1419.

• Geometry of Teichmüller curves (pdf), Oberwolfach Rep. 8 (2011), no. 2.

• Square-tiled surfaces and rigid curves on moduli spaces (pdf), Adv. Math. 228 (2011), no. 2, 1135-1162.

• Hilbert scheme of a pair of codimension two linear subspaces (with I. Coskun and S. Nollet) (pdf),  Comm. Algebra 39 (2011), no. 8, 3021-3043.

• Covers of elliptic curves and the moduli space of stable curves (pdf), J. Reine Angew. Math. 649 (2010), 167-205.

• Stable base locus decompositions of Kontsevich moduli spaces (with I. Coskun) (pdf), Michigan Math. J. 59 (2010), no. 2, 435-466.

• Linear series on ribbons (pdf), Proc. Amer. Math. Soc. 138 (2010), no. 11, 3797-3805.

• On the dimension of the Hilbert scheme of curves (pdf), Math. Res. Lett. 16 (2009), no. 6, 941-954.

• Mori's program for the Kontsevich moduli space (pdf), Int. Math. Res. Not. (2008), rnn 067, 17 pp.

• Covers of elliptic curves and the lower bound for slopes of effective divisors on the moduli space of curves (pdf), Ph.D. Thesis, Harvard University, 2008.

My papers are also available on arXiv. See above for updated versions.

Events:

• Riemann Surfaces: Random, Flat, and Hyperbolic Geometry, MFO, 9/8-13, 2024. 

• International Congress of Basic Science, Beijing, 7/14-26, 2024. 

• The 4th National Algebraic Geometry Conference, Weihai, 7/14-19, 2024. 

• Geometry and Moduli, Zhejiang University, 7/1-12, 2024. 

• Geometric, Algebraic, and Physical structures around the moduli of Meromorphic Quadratic Differentials, Stony Brook, 5/13-6/21, 2024. 

• Boston Algebraic Geometry Day, Tufts University, 4/20, 2024. 

• Geometry, Physics, and Representation Theory Seminar, Northeastern University, 3/28, 2024. 

• Algebraic Geometry NorthEastern Series, Boston College, 3/15-17, 2024. 

• Algebraic Geometry Seminar, UIC, 3/4, 2024. 

• Boston College Algebraic Geometry Seminar

• Boston College Geometry/Topology/Dynamics Seminar

• Harvard-MIT Algebraic Geometry Seminar